trignometry: prove that 1/sin2A+Cos4A/Sin4A=CotA-Cosec4A.
Answers
Answered by
34
Step-by-step explanation:
Take LHS...
= 1/Sin2A+Cos4A/Sin4A
= 2cos2A/(2cos2A.sin2A) + cos4A/sin4A
= 2cos2A/sin4A + cos4A/sin4A
= (2cos2A + 2cos²(2A) - 1)/sin4A
= 2cos2A(1+cos2A)/sin4A - 1/sin4A
= 2cos2A(1+2cos²(A) - 1)/(2cos2A.sin2A) - 1/sin4A
= 2cos²(A)/sin(2A) - 1/sin4A
= 2cos²A/(2cosA.sinA) - 1/sin4A
= cosA/sinA - 1/sin4A
= cotA - cosec(4A) = RHS
Hence, proved.....
Hope it helps you....
Similar questions